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@PHDTHESIS{Esser:672413,
      author       = {Esser, Patrick},
      othercontributors = {Reusken, Arnold and Behr, Marek},
      title        = {{P}arallele {V}erfahren höherer {O}rdnung zur {L}ösung
                      von {Z}weiphasen-{S}trömungen},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2016-08059},
      pages        = {1 Online-Ressource (x, 141 Seiten) : Illustrationen,
                      Diagramme},
      year         = {2016},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2016},
      abstract     = {Numerical methods for the simulation of twophase fluid
                      flows are discussed within this work. We focus on the
                      efficiency of these methods: higher order approximation of
                      the error bounds is achieved, as well as fast results on
                      modern computer architectures. The underlying model consists
                      of the incompressible twophase Navier-Stokes equations. The
                      phase boundary is described implicitly by a Levelset
                      technique. The surface tension is modeled as a localized
                      force term on the phase boundary.To set up the problem, we
                      first intoduce the governing Navier-Stokes equations. We
                      proceed afterwards with the numerical treatment of
                      stationary twophase flows to give an overview of the used
                      numerical techniques, e.g. spatial discretization of the
                      surface tension force with the Laplace-Beltrami approach.
                      During this overview we present the important technique
                      “Extended Finite Elements” (XFEM), which helps by
                      achieving an accurate spatial discretization of the jump in
                      the pressure variable.Following this introduction, the work
                      is structured in two main parts: first, the development and
                      analysis of a suitable time discretization method, based on
                      well known $\theta$-methods; second, the transfer of the
                      numerical methods on modern parallel computers.Regarding the
                      time integration, we restrict ourselves to a reduced
                      simplified model problem, which allows us to achieve optimal
                      error bounds (in a suitable weak norm). These error bounds
                      are also valid within realistic numerical simulations, the
                      results of a simulated rising butanol droplet in water are
                      presented. Additionally, we show some modification of these
                      methods, which ensures better numerical properties, e.g.
                      better stability.The second part of this work deals with the
                      parallelization and the modification/adaptation of numerical
                      methods for twophase flows on recent hardware architectures.
                      In cooperation with the center of scientific computing of
                      the RWTH Aachen, we have implemented the extension DiST
                      (Distributed Simplex Types) of the solver DROPS, developed
                      at the chair for numerical mathematics (RWTH Aachen). The
                      aim of DiST is the management of distributed simplexes. With
                      this library, it is possible to add MPI-parallel components
                      to DROPS, like efficient parallel hierarchical adaptive grid
                      structures or preconditioners of the iterative solvers.
                      These concepts are successfully applied up to 65.000
                      threads. Eventually, the shared memory parallelization of
                      DROPS is also discussed.},
      cin          = {111710 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)111710_20140620$ / $I:(DE-82)110000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:hbz:82-rwth-2016-080590},
      url          = {https://publications.rwth-aachen.de/record/672413},
}